Download Chapter 2 Angles and shapes

1
WORK PROGRAM  MQ 9 NSW 5.1 pathway
Chapter 2 Angles and shapes
Strand: Space and geometry
Substrands and Outcomes:
Two-dimensional space
SGS3.2a Manipulates, classifies and draws two-dimensional shapes and describes their features
Two-dimensional space
SGS3.2b Measures, constructs and classifies angles
Angles
SGS4.2 Identifies and names angles formed by the intersection of straight lines, including those related to
transversals on sets of parallel lines, and makes use of the relationships between them
Properties of geometrical figures
SGS4.3 Classifies, constructs and determines the properties of triangles and quadrilaterals
Section
Are you ready? (page 44)
GC tips, Investigations,
History of mathematics,
Maths Quest challenge,
10 Quick Questions,
Code puzzles
SkillSHEETS,
WorkSHEETS,
Interactive games,
Test yourself, Topic tests
(CD–ROM)
SkillSHEETS (page 44)
2.1: Classifying angles
2.2: Classifying triangles
according to the lengths
of their sides
2.3: Naming angles
2.5: Complementary
angles
2.6: Supplementary angles
2.13: More angle relations
Technology applications
(CD–ROM)
Learning outcomes
SGS3.2a
 naming isosceles,
equilateral and scalene
triangles
SGS3.2b
 classifying angles as
right, acute, obtuse,
reflex, straight or a
revolution
SGS4.2
 naming angles using
A and XYZ
notation
 identifying angles of a
complete revolution,
embedded in a diagram
 using the words
2
Triangles (page 45)
WE 1a-b, 2
Ex 2A Triangles (page 47)
SkillSHEET 2.1:
Classifying angles
(page 48)
SkillSHEET 2.2:
Classifying triangles
according to the lengths
of their sides (page 48)
Cabri geometry:
Classifying triangles
(sides) (pages 45, 48)
Cabri geometry:
Classifying triangles
(angles) (pages 46, 48)
Mathcad: Classifying
triangles (page 48)
‘complementary’ and
‘supplementary’ for
angles adding up to
90 and 180
respectively, and the
terms ‘complement’
and ‘supplement’
 establishing and using
the equality of
vertically opposite
angles
SGS4.3
 naming triangles (eg
ABC) in text
SGS4.2
 using the common
conventions to indicate
right angles and equal
angles on diagrams
SGS4.3
 using the common
conventions to mark
equal intervals on
diagrams
 recognising and
classifying types of
triangles on the basis
of their properties
 constructing various
types of triangles using
geometrical
instruments, given
3
Angles in a triangle
(page 50)
WE 3, 4, 5
Ex 2B Angles in a triangle
(page 52)
Maths Quest challenge:
Q1 (page 53)
SkillSHEET 2.3: Naming
angles (page 52)
SkillSHEET 2.4: Angles in
a triangle (page 52)
Cabri geometry: Angle
sum of a triangle
(page 52)
Mathcad: Angles in a
triangle (page 52)
Cabri geometry: Angles in
right-angled triangles
(page 52)
Exterior angles of a
triangle (page 54)
Investigation: Exterior
angles of a triangle
SkillSHEET 2.5:
Complementary angles
Cabri geometry: Exterior
angles of a triangle
different information
 recognising that a
given triangle may
belong to more than
one class (Reasoning)
SGS4.2
 labelling and naming
angles using A and
XYZ notation
 using dynamic
geometry software to
investigate angle
relationships (Applying
strategies, Reasoning)
SGS4.3
 labelling and naming
triangles (eg ABC) in
text and on diagrams
 justifying informally
that the interior angle
sum of a triangle is
180
 applying geometrical
facts, properties and
relationships to solve
numerical problems
such as finding
unknown angles in
diagrams (Applying
strategies)
SGS4.2
4
WE 6a-b, 7, 8
Ex 2C Exterior angles of a
triangle (page 56)
Constructing triangles
(page 58)
WE 9, 10, 11
Ex 2D Constructing
triangles (page 60)
(page 54)
(page 56)
SkillSHEET 2.6:
Supplementary angles
(page 56)
(pages 54, 56)
Mathcad: Exterior angles
of a triangle (page 56)
SkillSHEET 2.7:
Measuring and drawing
lines (page 60)
SkillSHEET 2.8:
Constructing angles with
a protractor (page 60)
WorkSHEET 2.1 (page 60)
Cabri geometry: Three
sides (page 60)
Cabri geometry: Two
angles and a side
(page 60)
Cabri geometry: Two
sides and an angle

labelling the vertex
and arms of an angle
with capital letters
 labelling and naming
angles using A and
XYZ notation
 using dynamic
geometry software to
investigate angle
relationships (Applying
strategies, Reasoning)
SGS4.3
 justifying informally
that any exterior angle
equals the sum of the
two interior opposite
angles
 applying geometrical
facts, properties and
relationships to solve
numerical problems
such as finding
unknown angles in
diagrams (Applying
strategies)
SGS4.3
 constructing various
types of triangles using
geometrical
instruments, given
different information
5
Quadrilaterals (page 61)
WE 12a-b
Ex 2E Constructing
triangles (page 62)
Maths Quest challenge:
Q1 (page 63)
10 Quick Questions 1
(page 64)
between (page 60)
Cabri geometry: Squares
(page 61)
Cabri geometry:
Rectangles (page 61)
Cabri geometry:
Rhombuses (page 61)
Cabri geometry:
Parallelograms (page 61)
Cabri geometry:
Trapeziums (page 61)
Cabri geometry: Kites
(page 61)
Cabri geometry: Types of
quadrilaterals (page 62)
Mathcad: Classifying
quadrilaterals (page 62)
SGS4.2
 using common
symbols for ‘is parallel
to’ (  ) and ‘is
perpendicular to’ (  )
SGS4.3
 using the common
conventions to mark
equal intervals on
diagrams
 constructing various
types of quadrilaterals
 investigating the
properties of special
quadrilaterals
 investigating the line
symmetries and the
order of rotational
symmetry of the
special quadrilaterals
 classifying special
quadrilaterals on the
basis of their
properties
 using dynamic
geometry software to
investigate the
properties of
geometrical figures
(Applying strategies,
Reasoning)
6
Angles in a quadrilateral
(page 65)
WE 13, 14
Ex 2F Angles in a
quadrilateral (page 66)
Angles and parallel lines
(page 68)
WE 15a-b, 16
Ex 2G Angles and parallel
lines (page 71)
Investigation: Angle
relationships with
parallel lines (page 69)
Maths Quest challenge:
Q1-2 (page 73)
Investigation: Geometry
and the Sydney Harbour
Bridge (page 74)
SkillSHEET 2.9: Angle
sum of a quadrilateral
(page 66)
Game time 001 (page 67)
WorkSHEET 2.2 (page 67)
Cabri geometry: Angles in
a quadrilateral (page 65)
Mathcad: Angles in a
quadrilateral (page 66)
Cabri geometry: Angle
sum of a quadrilateral
(page 66)
Cabri geometry: Angles in
a quadrilateral (page 66)
SkillSHEET 2.10: Angles
and parallel lines
(page 71)
Cabri geometry:
Corresponding angles
(page 68)
Cabri geometry: Cointerior angles (page 69)
Cabri geometry: Alternate
angles (page 69)
Cabri geometry: Parallel
SGS4.2
 using dynamic
geometry software to
investigate angle
relationships (Applying
strategies, Reasoning)
SGS4.3
 distinguishing between
convex and nonconvex quadrilaterals
 establishing that the
angle sum of a
quadrilateral is 360
 investigating the
properties of special
quadrilaterals
 applying geometrical
facts, properties and
relationships to solve
numerical problems
such as finding
unknown angles in
diagrams (Applying
strategies)
SGS4.2
 labelling and naming
angles using A and
XYZ notation
 identifying and naming
a pair of parallel lines
and a transversal
7
Code puzzle (page 75)
10 Quick Questions 2
(page 76)
lines (pages 69, 71)







using common
symbols for ‘is parallel
to’ (  ) and ‘is
perpendicular to’ (  )
using the common
conventions to indicate
parallel lines on
diagrams
identifying, naming
and measuring the
alternate angle pairs,
the corresponding
angle pairs and the cointerior angle pairs for
two lines cut by a
transversal
recognising the equal
and supplementary
angles formed when a
pair of parallel lines
are cut by a transversal
using angle properties
to identify parallel
lines
using angle
relationships to find
unknown angles in
diagrams
finding the unknown
angle in a diagram
using angle results,
giving reasons
8
Parts of a circle (page 77)
WE 17
Ex 2H Parts of a circle
(page 79)
Angle review (page 80)
Ex 2I Angle review
(page 80)
SkillSHEET 2.11: Using a
pair of compasses to
draw circles (page 79)
SkillSHEET 2.12:
Measuring angles with a
protractor (page 79)
Game time 002 (page 79)
Maths Quest challenge:
Q1 (page 83)
Investigation:
SkillSHEET 2.13: More
angle relations (page 80)
WorkSHEET 2.3 (page 83)
(Applying strategies,
Reasoning)
 using dynamic
geometry software to
investigate angle
relationships (Applying
strategies, Reasoning)
SGS3.2a
 creating circles by
finding points that are
equidistant from a
fixed point
 identifying and naming
parts of a circle,
including the centre,
radius, diameter,
circumference, sector,
semi-circle and
quadrant
SGS4.2
 labelling and naming
points, lines and
intervals using capital
letters
SGS4.3
 identifying and naming
parts of the circle and
related lines, including
arc, tangent and chord
SGS4.2
 identifying and naming
adjacent angles,
9
Parliamentary question
time (page 83)





vertically opposite
angles, straight angles
and angles of complete
revolution, embedded
in a diagram
using the words
‘complementary’ and
‘supplementary’ for
angles adding up to
90 and 180
respectively, and the
terms ‘complement’
and ‘supplement’
establishing and using
the equality of
vertically opposite
angles
identifying, naming
and measuring the
alternate angle pairs,
the corresponding
angle pairs and the cointerior angle pairs for
two lines cut by a
transversal
recognising the equal
and supplementary
angles formed when a
pair of parallel lines
are cut by a transversal
using angle properties
to identify parallel
10
lines
 using angle
relationships to find
unknown angles in
diagrams
 finding the unknown
angle in a diagram
using angle results,
giving reasons
(Applying strategies,
Reasoning)
SGS4.3
 using a parallel line
construction, to prove
that the interior angle
sum of a triangle is
180
 proving, using a
parallel line
construction, that any
exterior angle of a
triangle is equal to the
sum of the two interior
opposite angles
Summary (page 84)
Chapter review (page 86)
‘Test yourself’ multiple
choice questions
(page 88)
Topic tests (2)